Problem: Simplify the following expression: $\sqrt{40} + \sqrt{160}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{40} + \sqrt{160}$ $= \sqrt{4 \cdot 10} + \sqrt{16 \cdot 10}$ Separate the radicals and simplify. $= \sqrt{4} \cdot \sqrt{10} + \sqrt{16} \cdot \sqrt{10}$ $= 2\sqrt{10} + 4\sqrt{10}$ Finally, simplify by combining the terms. $= ( 2 + 4 )\sqrt{10} = 6\sqrt{10}$